In such spinning machines full bobbins are removed as a rule while the machine operates in a so-called "random exchange", and are replaced by empty bobbins. Since the timing of the bobbin exchange and the bobbins which have to be replaced are largely determined at random, the machine has to be capable of carrying out this exchange automatically and at each spooling position, independently from other spooling positions. The resulting achieved advantage is the elimination of waiting time for the services of an operator or a robot. This again avoids standstill and loss of thread material when a bobbin is removed, or excessive length on the bobbins when they continue to run until they are replaced.